Rolling element bearing for ultra-low viscosity fluids

ABSTRACT

A rolling element having comprises an inner ring, an outer ring and a series of rolling elements which are in contact with the raceways of the rings, an ultra-low viscosity fluid being present in the contacts having a kinematic viscosity ν=(η o /ρ) of less than 2 mm 2 /s, wherein the surfaces of the rings and the rolling elements have asperities which can have solid-to-solid contact during operation of the bearing. A factor &lt;i&gt;D q &lt;/i&gt; is defined which is equal to (I) whereby the solid-to-solid contact of the asperities is reduced by selecting such design parameters and operating conditions of the bearing that &lt;i&gt;D q &lt;/i&gt; is in the range from 8.0×10 −6  mrad s 1/2  to 1.36×10 −4  mrad s 1/2 .

[0001] The invention is related to a rolling element bearing, comprisingan inner ring, an outer ring and a series of rolling elements which arein contact with the raceways of said rings, an ultra-low viscosity fluidbeing present in said contacts having a kinematic viscosity ν=(η_(o)/ρ)of less than 2 mm²/s wherein the surfaces of the rings and the rollingelements have asperities which can have solid-to-solid contact duringoperation of the bearing.

[0002] Such a bearing is disclosed in U-B1-6,176,092. It is carried outas a hybrid 110 bearing having ceramic rolling elements and steel rings.The bearing in question is applied in a chiller, which means that anultra-low viscosity pure refrigerant is used as lubricant. Although suchultra-low viscosity refrigerants are only able to provide a relativelythin film under rolling action, nevertheless an acceptable service lifeof the bearing in question can be obtained.

[0003] This is to be attributed to the fact that the contacts betweenthe surface asperities of the rolling elements and the rings do not leadto welding phenomena as could be the case in all steel bearings. Despitethe fact that contacts do occur between the rolling elements and rings,welding is avoided as a result of the fact that the rolling elementsconsist of a ceramic material.

[0004] Ultra-low viscosity fluids (ULVF) used in rollingelement-bearings are defined as hydrocarbon-derived compounds withkinematic viscosity lower than, about 2 mm2/s (at room temperature, seeTable 1). There are many industrial applications that involvetransportation, processing or use of these fluids in a mechanicalsystem. Due to the very low viscosity of these fluids, total separationof ultra-low viscosity fluids from the lubrication system is notpossible using to day sealing technology. This leads to ultra-lowviscosity fluids pollution of the bearing lubricant, causing reductionof the oil film and increased direct metal-to-metal contact in therolling contact. This condition leads to a dramatic shortening of thelife of the rolling element bearing. Typically a factor 10 to 100 inlife reduction can be expected for these operating conditions. Todaythis problem is not solved in a satisfactory way. Present solutions haveattempted, in various ways, to limit as much as possible the presence ofultra-low viscosity fluids in the bearing space in order to reduce thesurface distress associated with mix lubrication operating conditionscaused by the presence of ultra-low viscosity fluids in the bearing,thus allowing the bearing to reach a minimum level of life expectancy.However in general this type of design increases the complexity and costof the machine and reduces its efficiency. During the years other ideaswere attempted to try to extend the life and reliability of a mechanicalsystem working in combination with ultra-low viscosity fluids. Thisincludes the use of hydrostatic supported journal bearings or use ofstandard hybrid bearings.

[0005] Nevertheless, it appears that still no general practical solutionexists which provides a significant extension of the service life and anacceptable reliability of rolling element bearings which operate inultra-low viscosity fluid lubrication conditions. Examples of suchultra-low viscosity fluids are shown in Table 1. TABLE 1 TypicallyUltra-low viscosity fluids. Kinematic Viscosity, mm²/sPressure-viscosity Fluid (liquid) Temperature, ° C. ν = η_(o)/ρcoefficient l/GPa α diesel 25 1.82-3.75  8.0-10.1 gasoline 25 0.46-0.556.3-7.1 ethanol 25 1.4 6.6 methanol 25 0.69 4.8 toluene 25 0.56 6.2decane 25 1.01 10.6 R134a 40 0.15 14.2 R124 40 0.17 15

[0006] Traditionally, it is attempted to prevent solid-to-solid contactof the surface asperities by ascertaining a certain level of separationbetween these surfaces. This separation depends on the ratio λ of thelubricant film thickness over the average roughness R_(q). For instance,it is generally accepted that for λ≦1 a great amount of surface contactoccurs, whereas for λ≧4 no surface contacts at all occur.

[0007] However, it has become clear that quantifying the separationbetween the surfaces by means of λ does not lead to a proper descriptionof ultra-low viscosity fluid lubricated bearings. This is due to thefact that according to this traditional approach of the phenomena whichoccur in a rolling contact bearing, no account is taken of the fact thatelastic deformations occur during over-rolling in the Hertzian contact.In particular, the fact is overlooked that as a result of asperitiesdeformation, the actual roughness heights in the rolling contact arereduced significantly, which leads to a better separation.

[0008] The object of the invention is to provide a rolling elementbearing of the type described before, which allows a better and morereliable service even under ultra-low viscosity fluid lubrication, e.g.as occur in the presence of pure refrigerant. This object is achieved inthat a factor D_(q) is defined which is equal to

Δ_(q){square root}{square root over (η_(o)α)}

[0009] wherein

[0010] Δ_(q)=mean slope of the roughness,

[0011] η_(o)=dynamic viscosity at saturation conditions,

[0012] α=pressure-viscosity coefficient,

[0013] and in that the solid-to-solid contact of the asperities isreduced by selecting such design parameters and operating conditions ofthe bearing that 8.0×10⁻⁶ mrad s^(1/2)≦D_(q)≦1.36×10⁻⁴ mrad s^(1/2).

[0014] By means of the factor D_(q) according to the invention, a rangeof design parameters can be selected in combination with a range ofoperating conditions which provide an increased separation of thecontact surfaces in the rolling contacts. Thereby, a significantincrease in reliability and service life expectancy of the bearings inquestion are obtained. This is a result of the fact that a drasticreduction of solid-to-solid contacts in the Hertzian zone is obtained.Thus, the occurrence of surface distress is greatly reduced, whereby therisk of raceway and rolling element surface damage is reduced as well.

[0015] Additional features can be incorporated in the bearing accordingto the invention so as to cope with short periods of reduced fluid flowof the ultra-low viscosity fluid. For instance, the surfaces of therings and/or of the rolling elements can be coated with a diamond likecoating (DLC), or the surfaces of the rings and/or of the rollingelements are coated with an anti-corrosion material. The surfaces inquestion could be of zinc or stainless steel.

[0016] Preferably, surfaces of the rings and/or of the rolling elementsare coated with an anti-corrosion material. For instance, all rollingelements are of a ceramic material. The rolling elements are separatedby a cage of a high temperature resistant material, e.g. a polymer(PEEK) or metal (brass).

[0017] The invention will now be described further with reference to anelucidation of the derivation of the factor D_(q) shown in the figures.

[0018]FIG. 1 shows a graph related to the amplitude reduction curveunder pure rolling.

[0019]FIG. 2 shows a graph of the relationship between the roughnesswavelength and slope for a sinusoidal waviness.

[0020]FIG. 3 shows a graph with representative ∇-values for two examplebearings.

[0021]FIG. 4 shows a graph of the specific film thickness λ as functionof the lubricant viscosity μ_(o) of the two bearings which have beenanalysed, a third hypothetic bearing has been included for comparisonreasons.

[0022]FIG. 5 shows a graph concerning the overall mechanism of roughnesselastic deformation.

[0023]FIG. 6 shows a graph concerning the probability of no-contact as afunction of the rolling velocity of the bearings.

[0024]FIG. 7 shows a graph related to the elastic deformation ratio oftwo surfaces as a function of D_(q) for an ULVF.

[0025]FIG. 8 shows a graph related to the amplitude reduction in puresliding.

[0026]FIG. 9 shows the principle of a hydrodynamic wedge.

[0027] In pure rolling, a surface topography made of long wavelengths(ω) components (low slopes, Δ_(q)) together with adequate operatingconditions favors elastic deformation and reduces the possibility ofsolid-to-solid contact, see FIG. 1.

[0028] The abscissa and the ordinate are defined as: $\begin{matrix}{\nabla{= \frac{\omega \sqrt{F}}{a\sqrt{2E^{\prime}\alpha \quad \eta_{o}\overset{\_}{u}\quad R_{x}}}}} & (1) \\{\frac{A_{d}}{A_{i}} = \frac{1}{1 + {0.15\quad {\nabla{+ 0.015}}\quad \nabla^{2}}}} & (2)\end{matrix}$

[0029] wherein:

[0030] F=contact force,

[0031] E′=combined elasticity modulus,

[0032] α=pressure-viscosity coefficient,

[0033] {overscore (u)}=average velocity of the surfaces,

[0034] R_(x)=reduced radius of curvature in the contact,

[0035] η_(o)=dynamic viscosity at saturation conditions,

[0036] a=semi-width of the Herzian contact along the rolling direction.

[0037] Small values of αη_(o) increase the elastic deformation of theroughness, which favors the separation of the surfaces. However, therebyalso the film thickness is reduced which possibly results in an overallreduction of the specific film thickness λ=h_(min)/σ. A compromise canbe found by increasing the wavelength of the roughness ω, so that itallows even more deformation to keep an acceptable value of λ.

[0038] In practical situations, real roughness can be regarded (usingFourier Decomposition) as the addition of many sinusoidal (or in 2-Dbi-sinusoidal) waves with different amplitudes. So each component isreduced according to equation (2) with ∇ given by the specificwavelength co as pointed by equation (1). So, in fact the whole ∇spectrum is covered in real roughness.

[0039] To understand the relationship between the representativewavelength as measured by using standard ISO parameters (Δ_(q), R_(q),etcetera) in real surfaces and the representative slope of the surface,it can be assumed that the real roughness can be represented by a singlesinusoidal wave z(x) of wavelength ω, as shown in FIG. 2. Therefore,$\begin{matrix}{{z(x)} = {A\quad {\sin \left( \frac{2\pi \quad x}{\omega} \right)}}} & (3)\end{matrix}$

[0040] with slopes given by dz/dx, $\begin{matrix}{{\tan (\theta)} = {\phi = {\frac{2\quad \pi \quad A}{\omega}{\cos \left( \frac{2\pi \quad x}{\omega} \right)}}}} & (4)\end{matrix}$

[0041] and the curvature by, d²z/dx², $\begin{matrix}{C = {\frac{4\quad \pi^{2}A}{\omega^{2}}{\sin \left( \frac{2\pi \quad x}{\omega} \right)}}} & (5)\end{matrix}$

[0042] From equation (4),${\omega = \frac{2\quad \pi \quad A}{\tan \quad \theta}},$

[0043] in a real surface, A is represented by R_(q) and tanθ isrepresented by tanΔ_(q), therefore, $\begin{matrix}{\omega = \frac{2\quad \pi \quad R_{q}}{\tan \quad \Delta_{q}}} & (6)\end{matrix}$

[0044] From equation (6) it can be seen that for roughness with the sameR_(q), a lower value of Δ_(q) will increase the representativewavelength ω, from equation (1) this increases ∇ and therefore theelastic deformation of the surfaces is also increased, equation (2).

[0045] Based on this approach, an example comparison is made for a“Normal” vs. “Improved” angular contact bearing.

[0046] The internal geometry of a deep grove ball bearing (DGBB)nomination 71928 is selected, wherein the “normal” bearing (suffix 1) isan all-steel bearing with normal lubrication conditions lubricated withoil ISO 68 and the “improved” bearing (suffix 2) is a hybrid bearing(ceramic balls and steel rings) lubricated with ultra-low viscosityfluid.

[0047] The operating conditions are defined as follows:

[0048] F=530 N (heaviest loaded contact),

[0049] {overscore (u)}=15.43 m/s,

[0050] R_(x)=7.174 mm,

[0051] E′₁=226.4×10⁹ Pa (all-steel)

[0052] E′₂=271.1×10⁹ Pa (hybrid)

[0053] a₁=0.17 mm (all-steel)

[0054] a₂=−0.14 mm (hybrid),

[0055] Δ_(q1)=16.11 mrad (all-steel),

[0056] Δ_(q2)=9.11 mrad (hybrid),

[0057] both bearings with R_(q)≈0.08 μm.

[0058] The lubricant properties are defined as follows:

[0059] Oil Properties:

[0060] η_(o)=0.0585 Pa s,

[0061] α=30×10⁻⁹ Pa⁻¹ (oil),

[0062] Ultra-low viscosity fluid properties:

[0063] η_(o)=214.5×10⁻⁶ Pa s,

[0064] α=15×10⁻⁹ Pa⁻¹ (ultra-low viscosity liquid).

[0065] For this example, FIG. 3 shows the representative values of ∇ inboth cases, one can see that for the hybrid bearing (improved) theelastic deformation of the roughness is larger than the all-steelbearing.

[0066] To have a clear idea of the contribution on the surfaceseparation of this elastic deformation, the specific film thickness or λshould be considered. The specific film thickness is defined byλ=h/R_(q), where h is the chosen film thickness, for comparison reasonsit can be either the minimum film thickness in the contact or thecentral film thickness, here the central film thickness has been used.In general, it is accepted that for λ≦1 there is great amount of surfacecontact while for λ>4 there is no contact at all between the surfaceasperities.

[0067]FIG. 4 shows the variations of λ as a function of the viscosity ofthe fluid no for the two bearings given in the example. For comparison,the results of a hypothetic hybrid bearing with a Δ_(q) value same asthe “normal” all-steel bearing have been included. From this comparison,one can see the contribution to the improvement of λ just due to thereduction of Δ_(q) in the improved bearing, especially in the lowviscosity region.

[0068]FIG. 5 shows in schematic way the overall effect of the inventionin the bearing surfaces. By calculating the “bearing area curve” of thesurfaces of the two bearings, it is possible to estimate the probabilityof no contact (ratio of surface area with heights lower than h oversurface area exceeding h). FIG. 6 shows this ratio as a function of thespeed in the two bearings.

[0069] The D_(q) Parameter will now be derived. From the above section,it is clear that the variable ∇ describes the amount of elasticdeformation of the roughness, equation (2). However, in a simpler case,assume two bearings with the same material and equal operatingconditions but different lubricant viscosities and roughness wavelength.From equation (1), the ration of ∇ can then be reduced to:$\begin{matrix}{\frac{\nabla_{1}}{\nabla_{2}} = \frac{{\omega_{1}\left( \sqrt{\eta_{o}\alpha} \right)}_{2}}{{\omega_{2}\left( {\sqrt{\eta_{o}}\alpha} \right)}_{1}}} & (7)\end{matrix}$

[0070] now, by substituting (6) into (7), and assuming equal R_(q)values and only different slopes in the roughness one obtains,$\begin{matrix}{\frac{\nabla_{1}}{\nabla_{2}} = \frac{\left( \sqrt{\eta_{o}\alpha} \right)_{2}\tan \quad \Delta_{q2}}{\left( {\sqrt{\eta_{o}}\alpha} \right)_{1}\tan \quad \Delta_{q1}}} & (8)\end{matrix}$

[0071] Finally, since the angle Δ_(q) is in general very small, so thattanΔ_(q)≈Δ_(q), then $\begin{matrix}{\frac{\nabla_{1}}{\nabla_{2}} = \frac{\left( \sqrt{\eta_{o}\alpha} \right)_{2}\quad \Delta_{q2}}{\left( {\sqrt{\eta_{o}}\alpha} \right)_{1}\quad \Delta_{q1}}} & (9)\end{matrix}$

[0072] From equation (9), it is clear that in this case the parameterthat determines the amount of deformation in the roughness under equaloperating conditions and material is only

D _(q)=Δ_(q){square root}{square root over (η_(o)α)}  (10)

[0073] It has been found by calculations and tests that bearings with8.0×10⁻⁶ mrad s^(l/2)<D_(q)≦1.36×10⁻⁴ mrad s^(l/2) work well under ULVFlubrication conditions.

[0074] The following data have been used for the limits calculation:

[0075] Upper Limit:

[0076] Δ_(q)=18.11 mrad

[0077] α=15.0×10⁻⁹ Pa⁻¹

[0078] η_(o)=0.0038 Pa s

[0079] Lower Limit:

[0080] Δ_(q)=9.0 mrad

[0081] α=4.5×10⁻⁹ Pa⁻¹

[0082] η_(o)=167.1×10⁻⁶ Pa s

[0083] Just as a reference, the oil-lubricated all-steel bearing in theexample has D_(q)=6,75×10⁴ mrad s^(1/2) while the hybrid “improved”bearing of the same example has D_(q)=1.63×10⁻⁵ mrad s^(1/2).

[0084] The variable ∇ as a function of D_(q) can be written as:$\begin{matrix}{{\nabla{= \frac{C}{D_{q}}}}{{where},{C = \frac{2\quad \pi \quad R_{q}\sqrt{F}}{a\sqrt{2E^{\prime}\overset{\_}{u}\quad R_{x}}}}}} & (11)\end{matrix}$

[0085] The deformation ratio A_(r) for two surfaces can be obtained bydividing their A_(d)/A_(i) ratios, and using (11) one can write$\begin{matrix}{A_{r} = {\frac{\left( {A_{d}/A_{i}} \right)_{1}}{\left( {A_{d}/A_{i}} \right)_{2}} = \frac{1 + {0.15\left( {C/D_{q2}} \right)} + {0.015\left( {C/D_{q2}} \right)^{2}}}{1 + {0.15\left( {C/D_{q1}} \right)} + {0.015\left( {C/D_{q1}} \right)^{2}}}}} & (12)\end{matrix}$

[0086] This expression gives information on how much more elasticdeformation and “improved” surface can give as a function of D_(q) incomparison to another one.

[0087]FIG. 7 shows a plot of equation (12) for a fixed value ofD_(q)2=6.75×10⁻⁴ mrad s^(1/2), while D_(q1) was varied to cover theclaimed range 8×10⁻⁶ mrad s^(1/2)≦D_(q1)≦1.36×10⁻⁴ mrad s^(1/2), theconstant has also been fixed to the value of the all-steel bearing ofthe example C=3×10⁻⁴ mrad s^(1/2). From equation (12) one can see that(A_(d)/A_(i))=A_(r)(A_(d)/A_(i))₂, and always A_(r)<1.

[0088] The previous section refers to pure rolling, where equations (1)and (2) are valid. When sliding is present in the contact, a morecomplex situation arises since pressures and roughness change with time.However, the same basic principles of low slopes related to high elasticdeformation apply.

[0089] Consider the case of pure sliding, the elastic deformation of theroughness is governed by different principles, however, reducing theslopes also leads to more elastic deformation.

[0090]FIG. 8 shows a schematic reduction of the amplitude of thesinusoidal components in real roughness as a function of the wavelengthnumber “n”. Longer wavelengths deform more than short.

[0091] Long wavelengths in the surface topography also reduce thepressure ripple amplitude leading to lower subsurface stresses andtherefore longer life. $\begin{matrix}{p_{\max} = \frac{3}{2{H_{o}\left( {1 + H_{o}} \right)}\left( {1 + {2H_{o}}} \right)}} & (13)\end{matrix}$

[0092] From FIG. 9 it is clear that H_(o)=h_(o)/s_(h). Small values ofs_(h) produce large values of H_(o) and this makes p_(max) small.

1. Rolling element bearing, comprising an inner ring, an outer ring and a series of rolling elements which are in contact with the raceways of said rings, an ultra-low viscosity fluid being present in said contacts having a kinematic viscosity ν=(η_(o)/ρ) of less than 2 mm²/s, wherein the surfaces of the rings and the rolling elements have asperities which can have solid-to-solid contact during operation of the bearing, characterised in that a factor D_(q) is defined which is equal to Δ_(q){square root}{square root over (η_(o)α)} wherein Δ_(q)=mean slope of the roughness, η_(o)=dynamic viscosity at saturation conditions, α=pressure-viscosity coefficient, and in that the solid-to-solid contact of the asperities is reduced by selecting such design parameters and operating conditions of the bearing that D_(q) is in the range from 8.0×10⁻⁶ mrad s^(1/12) to 1.36×10⁻⁴ mrad s^(1/2).
 2. Bearing according to claim 1, wherein the surfaces of the rings and/or of the rolling elements are coated with a diamond like coating (DLC).
 3. Bearing according to claim 1, wherein the surfaces of the rings and/or of the rolling elements are coated with an anti-corrosion material.
 4. Bearing according to claim 3, wherein the anti-corrosion material is zinc.
 5. Bearing according to claim 3, wherein the anti-corrosion material is stainless steel.
 6. Bearing according to any of the preceding claims, wherein at least one of the rings and rolling elements have at least a ceramic rolling surface layer.
 7. Bearing according to any of the preceding claims, wherein all rolling elements are of a ceramic material.
 8. Bearing according to any of the preceding claims, wherein the rolling elements are separated by a cage of a high temperature resistant material, e.g. a polymer (PEEK) or metal (brass).
 9. Bearing according to any of the preceding claims, wherein the rings and rolling elements having a standard roughness R_(q) of maximally 0.1 μm, 